Lesson 2-6Algebraic Proofs

Ohio Content Standards:

Ohio Content Standards:Establish the validity of conjectures about geometric objects, their properties and relationships by counter-example, inductive and deductive reasoning, and critiquing arguments made by others.

Ohio Content Standards:Make and test conjectures about characteristics and properties (e.g., sides, angles, symmetry) of two-dimensional figures and three-dimensional objects.

Ohio Content Standards:Make, test and establish the validity of conjectures about geometric properties and relationships using counterexample, inductive and deductive reasoning, and paragraph or two-column proof.

Reflexive Property

Reflexive Property

For every number a = a.

Symmetric Property

Symmetric Property

For all numbers a and b, if a = b, then b = a.

Transitive Property

Transitive Property

For all numbers a, b, and c, if a = b and b = c, then a = c.

Addition and Subtraction Properties

Addition and Subtraction Properties

For all numbers a, b, and c, if a = b, then a + c = b + c and a – c = b – c.

Multiplication and Division Properties

Multiplication and Division Properties

For all numbers a, b, and c, if a = b, then a ∙ c = b ∙ c and if c = 0, .

c

b

c

a

Substitution Property

Substitution Property

For all numbers a and b, if a = b, then a may be replaced by b in any equation or expression.

Distributive Property

Distributive Property

For all numbers a, b, and c, a(b + c) = ab + ac.

Deductive Argument

Deductive Argument

A group of algebraic steps used to solve problems.

Solve.2(5 – 3a) – 4(a + 7) = 92

Two-Column Proof (Formal Proof)

Two-Column Proof (Formal Proof)

Contains statements and reasons organized in two columns.

Write a two-column proof.

.3 then ,64

37 If

d

d

Write a two-column proof.1. then ,111830 If ppp

Assignment:

Pgs. 97 - 100 14-23 all,

24-30 evens40-46 evens